The relative advantages and disadvantages of three different algorithms are compared for simulating the time evolution of two-dimensional line-edge profiles produced by a locally rate dependent surface etching phenomenon. Simulated profiles typical of optical projection printing and electron-beam and X-ray lithography of micron-sized lines in resist and etching of ion-implanted SiO2 are used as a basis of comparison. One of the algorithms is a cell-by-cell removal model used earlier by Neureuther and Dill. One of the newly developed algorithms employs ray tracing; it can be shown that the path followed by a point on a front between the developed and undeveloped regions can be calculated using ray-optic equations. The other new algorithm uses a string of points initially on the surface of the exposed resist. The points on the string advance perpendicular to the local direction of the string; with time the string of points moves down into the resist, replicating the action of a developer. We compare the computing cost, convenience, and accuracy of the algorithms.